A holiday park offers pony trips to children. There are 10 ponies, only two of which are suitable…

A holiday park offers pony trips to children. There are 10
ponies, only two of which are suitable for children under 5 years of age. Ten
per cent of children at the park are under 5.

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(a) If children turn up at random for these trips what is
the probability that there will be more than two children under fi ve in a group
of 10 children wanting to take the pony trip?

(b) As a result of a special promotion the proportion of
children under fi ve is 20%. Will the probability of more than two children in
a group of 10 change, and if so to what?

(c) Work out the mean and standard deviation of the
distributions in (a) and (b).